English

Norm-compatible systems of cohomology classes for $\operatorname{GU}(2,2)$

Number Theory 2018-07-19 v2

Abstract

We describe work of Faltings on the construction of \'etale cohomology classes associated to symplectic Shimura varieties and show that they satisfy certain trace compatibilities similar to the ones of Siegel units in the modular curve case. Starting from those, we construct a two variable family of trace-compatible classes in the cohomology of a unitary Shimura variety.

Keywords

Cite

@article{arxiv.1711.10571,
  title  = {Norm-compatible systems of cohomology classes for $\operatorname{GU}(2,2)$},
  author = {Antonio Cauchi},
  journal= {arXiv preprint arXiv:1711.10571},
  year   = {2018}
}

Comments

33 pages; title changed; in the current version, we construct a two variable family of norm-compatible classes in the cohomology of the Shimura variety for GU(2,2) (see Theorem B of the introduction), improving substantially Corollary B of the previous version